JP2011128675A - Processing system, method and program for modeling system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To automatically distinguish a simplifiable part of system representation by a quantitative reference, in a modeling tool for a design. <P>SOLUTION: An expression is extracted from a block of SysML, or a block diagram of Simulink (R) is converted into a differential equation, and a coefficient thereof is expanded in a series. First, the differential equation is normally solved by a CAS, and preferably, a solution thereof is also expanded in a series. Next, the expression including the differential equation is solved by the CAS as an interval coefficient by interval analysis technique. Coefficient vectors of the stored solution obtained by performing the normal solution and the solution of a result of the interval analysis are compared. As a result, when an inter-vector distance is a fixed value or below, a target coefficient is set to zero, and the expression including the differential equation is solved by the CAS. The coefficient vectors of the stored solution obtained by performing the normal solution and the solution of the result are newly compared. As a result, when the inter-vector distance is the fixed value or below, a term of the target coefficient is dropped from the differential equation to simplify the differential equation. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a modeling system for designing mechanical devices such as automobiles, robots, and aircraft, and more particularly to a system, method, and program for processing mathematical expressions used in the modeling system.

  Conventionally, models have been created and tested using simulation modeling tools such as MATLAB (R) / Simulink (R), and installed in actual machines. Modeling techniques using MATLAB (R) / Simulink (R) are described in many published publications such as JP-A-2005-222420.

  On the other hand, recently, as disclosed in Japanese Patent Application Laid-Open No. 2009-176010, modeling of a mechanism device is also performed using SysML, which is an extension of UML.

  In MATLAB (R) / Simulink (R), the behavior of a model is often reduced to a differential equation, and in UML / SysML, the behavior and constraints of model elements are described using mathematical expressions.

  At that time, typically, as described in JP-A-7-281714, how to deal with the described mathematical model continues to be a problem.

  By the way, when a system description designed based on a general evaluation function is used in concrete modeling in a control strategy for designing a product, a simpler expression can be made for a complex mathematical model. There is a desire to decide whether or not. This is because if a complicated mathematical model is set as it is, a complicated configuration may occur, and problems such as increased component costs and manufacturing costs may occur. Therefore, if equivalent functions can be described with a simplified mathematical model, it is very meaningful as a cost saving.

  However, in the control strategy design by SysML or the like, the problem is that the standard is unclear about the appropriateness of the detail of the system description by the mathematical formula or Simulink®.

  For example, the degree of detail in which a mathematical expression such as an internal block diagram is described as a constraint in SysML and a system element is described as a Simulink model is dependent on the aspect in which modeling is used or the subjectivity of the model creator.

  In addition, when modeling the control part of interest, the system description designed based on general evaluation criteria only gives a broad meaning to the modeling of the control object of interest, resulting in overly complex control. In order to avoid the possibility of designing the system and to avoid it, it is necessary to determine whether there is a simplification possible part based on the quantitative criteria.

  However, such techniques are not known until now.

JP-A-2005-222420 JP 2009-176010 A JP-A-7-281714

  An object of the present invention is to provide a technique that makes it possible to automatically determine a simplifiable part of a system expression based on a quantitative criterion in a modeling tool for design.

  Another object of the present invention is to quantitatively determine an unnecessarily complicated part as a part that can be simplified, thereby enabling efficient control system design while maintaining the physical meaning. There is to do.

  Still another object of the present invention is to make it possible to narrow down the actual operation area by optimizing the controller design.

  The present invention has been made to achieve the above object. According to the present invention, first, mathematical expressions are extracted from, for example, a SysML block by a computer process, or a block diagram of Simulink (R) is obtained. In any case, mathematical equations are prepared on a computer memory or hard disk.

  According to the present invention, the extracted coefficients of the mathematical formula that may include a differential equation are series-expanded. At this time, a suitable series expansion is a Volterra series expansion that is often used in nonlinear signal processing and the like.

  Next, the system of the present invention solves a mathematical expression including a differential equation by a known mathematical expression processing system (CAS). This solution is temporarily stored on a memory or hard disk.

  Next, the system of the present invention gives a disturbance to one coefficient of a mathematical expression including a differential equation that is series-expanded, and solves the mathematical expression including the differential equation by CAS as an interval coefficient by the technique of interval analysis.

  Next, the system of the present invention compares the solution of the result of the interval analysis and the stored coefficient vector of the normally solved solution to determine whether the inter-vector distance is equal to or less than a predetermined value. Otherwise, the next coefficient expanded from the series including the differential equation is selected, and if so, the target coefficient is set to 0 and the mathematical expression including the differential equation is solved by CAS.

  Again, the result solution is compared with the stored coefficient vector of the normally solved solution to determine whether the distance between the vectors is equal to or less than a predetermined value.

  If it is determined that the distance between vectors is equal to or less than a predetermined value, it is determined that the target coefficient can be omitted.

  According to another aspect of the present invention, the mathematical formula obtained above is converted back into a block diagram, and the block diagram is converted into a graph representation on a computer memory, and then topological The genus is determined. Then, the validity of the description of the block diagram is determined by determining that the genus is smaller than a certain number.

  According to the present invention, in the modeling tool for design, in the mathematical expression of the model, the terms that can be simplified in the system expression are automatically discriminated by the quantitative criterion by rationally omitting the term in consideration of stability. It becomes possible to do.

  Further, according to the invention, by simplifying mathematical expression expression, it is possible to efficiently determine an unnecessarily complicated part as a simplifiable part of the system, while maintaining the physical meaning and efficiently. Control system design can be performed.

It is a block diagram of an example of the hardware constitutions for carrying out this invention. It is a figure which shows the functional block diagram for implementing this invention. It is a figure which shows extraction of the numerical formula from the block of SysML, and extraction of the simplified numerical formula. It is a figure which converts a block diagram into a formula and converts a simplified formula into a block diagram. It is a figure which shows the flowchart of the process which simplifies numerical formula. It is a figure which shows the flowchart of the process which simplifies numerical formula. It is a figure which shows the flowchart of the process which discriminate | determines the kind of block diagram. It is a figure which shows the example which designs an H2 optimal controller.

  Embodiments of the present invention will be described below with reference to the drawings. Unless otherwise noted, the same reference numerals refer to the same objects throughout the drawings. It should be understood that what is described below is one embodiment of the present invention, and that the present invention is not intended to be limited to the contents described in this example.

  Referring to FIG. 1, there is shown a block diagram of computer hardware for realizing an example system configuration and processing for carrying out the present invention. In FIG. 1, a CPU 104, a main memory (RAM) 106, a hard disk drive (HDD) 108, a keyboard 110, a mouse 112, and a display 114 are connected to the system path 102. The CPU 104 is preferably based on a 32-bit or 64-bit architecture, such as Intel Pentium ™ 4, Core ™ 2 Duo, Xeon ™, AMD Athlon ™. Etc. can be used. The main memory 106 preferably has a capacity of 2 GB or more.

  Although not shown individually, the hard disk drive 108 stores an operating system in advance. The operating system can be any compatible with the CPU 104, such as Linux (trademark), Microsoft (trademark) Windows (trademark) 7, Windows XP (trademark), Windows (trademark) 2000, or Mac OS (trademark) of Apple Computer. Good.

  Hard disk drive 108 also includes IBM® Rational® Rhapsody®, a UML / SysML modeling system available from International Business Machines Corporation, and simulations available from MathWorks. -MATLAB (R) / Simulink (R), a modeling system, has been introduced. In the functional block diagram of FIG. 2, the UML / SysML modeling system is illustrated as block 202 and MATLAB® / Simulink® is illustrated as block 202.

  Further, Maxima is introduced into the hard disk drive 108 as a mathematical expression processing tool (CAS). The CAS that can be used in this embodiment is not limited to Maxima, and any CAS that can be used such as Maple available from MapleSoft or Mathematica available from Wolfram Research may be used. Alternatively, you can use the Symbolic Math Toolbox in the MATLAB ToolBox.

  The hard disk drive 108 further stores a source model file 206 for the UML / SysML modeling system 202 and a source code 208 for the simulation modeling system, shown in FIG. 2 and described in detail later. The

    The hard disk drive 108 further stores a mathematical expression extraction module 210, a mathematical expression conversion module 212, a section analysis module 214, a stability determination module 220, a mathematical expression injection module 224, a block diagram conversion module 226, and a genus determination module 228. If necessary, it is read out to the main memory 106 by the action of the operating system and executed.

  The keyboard 110 and the mouse 112 are loaded from the operating system or the hard disk drive 108 into the main memory 106, and are used to start a program (not shown) displayed on the display 114 and to input characters. .

  The display 114 is preferably a liquid crystal display, and can be of any resolution such as XGA (1024 × 768 resolution) or UXGA (1600 × 1200 resolution). Although not shown, the display 114 is used to display graph data to be processed and graph similarity.

  Next, a functional block diagram according to the present invention will be described with reference to FIG. As described above, the UML / SysML modeling system 202 is IBM® Rational® Rhapsody® in this embodiment, but is not limited thereto, and any UML / SysML modeling system can be used. Can be used.

  On the UML / SysML modeling system 202, the user can create a model of the design according to the rules of UML / SysML and save it as a model file 206 on the hard disk drive 108. It can also be read and edited at any time.

  Blocks 302, 304, and 306 in FIG. 3 show examples of SysML class diagrams.

  In this embodiment, the simulation modeling system 204 is MATLAB® / Simulink® as described above, but is not limited thereto, and any simulation modeling model such as open source Scilab / Scicos is used. It is possible to use a tool.

  On the simulation modeling system 204, the user can generate and save the source code 208 in the hard disk drive 108 by arranging and connecting the functional blocks by GUI operation. It can also be read and edited at any time. The source code 208 may include an MDL file for describing dependencies between functional blocks.

  The formula extraction module 210 extracts a formula or constraint formula that defines behavior from a specified block of the UML / SysML modeling system 202, and places it on the main memory 106, preferably for later processing. To do. In the example of FIG. 3, a mathematical expression (in this case, a differential equation) is included in the block 306 and is extracted as a mathematical expression 308 by the mathematical expression extraction module 210.

  The mathematical expression conversion module 212 has a function of converting a block diagram described in the simulation modeling system 204 into a corresponding differential equation and preferably placing it on the main memory 106. The mathematical expression conversion module 212 can basically be created by a program such as C, C ++, Java (R), or can be realized by a combination of Maple and MapleSim.

  FIG. 4A shows an example of a block diagram created by the simulation modeling system 204. The mathematical expression conversion module 212 converts the block diagram shown in FIG. 4A into a differential equation shown in FIG.

  The interval analysis module 214 expands the coefficient of the mathematical expression including the differential equation received from the mathematical expression extraction module 210 or the mathematical expression conversion module 212 using a function of CAS 216 in a Volterra series. The Volterra series expansion is described in JP-A-11-261436, JP-A-2006-86681, JP-A-2006-260244, JP-A-2006-28746, and the like. I will not explain in detail.

  The series expansion used in the present invention can use any series expansion such as Taylor expansion according to the purpose, in addition to the Volterra series expansion.

  The interval analysis module 214 also has a function of generating an interval generated based on a series expansion coefficient for interval analysis and passing it to the CAS 216.

  The CAS 216 expands the mathematical expression itself given from the mathematical expression extraction module 210 or the mathematical expression conversion module 212, or expands the differential equation solution to a Volterra series, and forms a series 218 in which the mathematical solution is expanded as a hard disk drive. Save to 108. The expanded series 218 includes Volterra series expansion data of coefficients of mathematical expressions including differential equations received from the mathematical expression extraction module 210 or the mathematical expression conversion module 212.

  The stability determination module 220 operates in cooperation with the interval analysis module 214 and the CAS 216 to obtain a simplified mathematical expression 222. The operation of the stability determination module 220 will be described in detail later with reference to the flowcharts of FIGS.

  As a result of the processing, the stability determination module 220 generates a simplified mathematical expression 222, and preferably arranges it in a predetermined area of the main memory 106. The simplified mathematical formula 222 is indicated by reference numeral 310 in the SysML block of FIG. 3 and is shown in FIG. 4C for Simulink®.

  The formula injection module 224 injects and overwrites the simplified formula 222 into the SysML block. In FIG. 3, a simplified formula 310 is injected into block 306.

  The block diagram conversion module 226 has a function of converting the simplified mathematical expression 310 shown in FIG. 4 (c) into a block diagram as shown in FIG. 4 (d). The conversion of such differential equations to block diagrams is made by expressing the differential equation as simplified expression 310 in MATLAB (R) and making it one of the blocks that can be used in Simulink called S-function. Is achieved. However, some manual processing may be required.

  The genus determination block 228 has a function of determining the validity of the block diagram by obtaining the genus of the block diagram converted from the differential equation as shown in FIG. The genus is a topological property and is the number of holes opened in a curved surface. More detailed processing of the genus determination block 228 will be described later in detail with reference to the flowchart of FIG.

  Next, the processing of the stability determination block of FIG. 2 will be described with reference to the flowcharts of FIGS. First, in the step of FIG. 5, whether the mathematical expression conversion module 212 converts the block diagram as shown in FIG. 4, or the mathematical expression extraction module 210 extracts the mathematical expression from the block as shown in FIG. A mathematical formula including a differential equation is prepared on the main memory 106.

のようになる。 In the following, a differential equation will be described as an example, but this also includes ordinary mathematical expressions. That is, when the differential equation is expressed as

become that way.

  That is, here, assuming that P (x) = Q (x) = 0, only R (x) remains, resulting in an ordinary mathematical expression that does not include a differential equation. Also, in this example, it is a first order differential equation, but it should be understood that it may be a higher order differential equation. However, differential equations up to second order are sufficient for most design purposes, as are Newton's equations. The differential equation may be a simultaneous differential equation as long as CAS can be solved.

  According to one embodiment of the present invention, such a differential equation is not solved by CAS 216 as it is, but the functions P (x), Q (x), R (x) of the differential equation are series expanded by the function of CAS 216. Is done.

この式で、実際は∞のところは、主記憶１０６のサイズの限界に基づく利用可能なメモリサイズに合わせて、適当な有限の項数で打ち切る。この式で、h_p(m₁,...,m_p)は、ボルテラ核(Volterra kernel)と呼ばれる。この実施例では、x(n-m_i) ( i = 1,...,p)としては、場合に応じて、指数関数、三角関数、代数関数などが使用される。 A series expansion suitable for the present invention is a Volterra series expansion generally used for analysis of nonlinear systems, and is generally expressed by the following equation.

In this equation, in fact, the part at ∞ is truncated with an appropriate finite number of terms in accordance with the available memory size based on the size limit of the main memory 106. In this equation, h _p (m ₁ , ..., m _p ) is called a Volterra kernel. In this embodiment, an exponential function, a trigonometric function, an algebraic function, or the like is used as x (nm _i ) (i = 1,..., P) depending on cases.

  Regarding the Volterra series expansion, several patent publications have already been cited as conventional techniques, but for more detailed techniques of Volterra series expansion, Analytical and Numerical Methods for Volterra Equations (Studies in Applied and Numerical Mathematics) by Peter See Linz (Hardcover-Jan 1, 1987).

  In addition, the preferred series expansion assumed in this embodiment is Volterra series expansion, but the present invention is not limited to Volterra series expansion, and other known series such as Taylor series expansion and Fourier series expansion may be used depending on the case. A series expansion of can also be used.

When each of P (x), Q (x), and R (x) is expanded by Volterra series,
Summarizing in terms of x (nm ₁ ) ... x (nm _p ), a sequence of coefficients including Volterra kernels is obtained for each of P (x), Q (x), and R (x).

Then, if the sequence of x (nm ₁ ) ... x (nm _p ) is a vector and written as X, then P (x) = pX, Q (x) with the coefficient vectors p, q, r = qX, R (x) = rX. Therefore, the components of the vectors p, q, and r are arranged and expressed as α.

  In step 504, CAS 216 solves the differential equation, and in one embodiment of the present invention, the solution is also denoted by βX in a Volterra series expansion. X here is the same as X described in P (x), Q (x), and R (x). The value of β is stored in an appropriate area of the main memory 106 for later reference.

In step 506, the interval analysis module 214 replaces one element α _{1 of the} vector α with an interval [α ₁ , δ] = α ₁ ± δ with some appropriate small disturbance value δ. With the vector α _I , CAS 216 again solves the differential equation. In this embodiment of the present invention, the solution is also expressed as β _I X by Volterra series expansion. The value of the vector β _I is stored in an appropriate area of the main memory 106 for later reference.

Interval analysis is a technique used in numerical calculations with guaranteed accuracy, and the basic operations are as follows.
[A, α] + [B, β] = [A + B, α + β]
[A, α]-[B, β] = [A-B, α + β]
[A, α] × [B, β] = [AB, A | β | + | B | α + αβ]
Furthermore, f ([A, α]) or the like can be defined for an arbitrary function f (x).
For more detailed techniques of interval analysis, refer to Modern Non-linear Science Series 6 “Numerical Calculations with Guaranteed Accuracy” by Shinichi Oishi, Corona, 2000, etc.

In step 508, the coefficient vector β _I of the solution obtained by the interval calculation is compared with the coefficient vector β of the solution obtained by the normal calculation. More specifically, given a distance function d (),
The value of d (β, β _I ) is calculated.

The preferred distance used here is the Mahalanobis distance based on the correlation between multiple variables, and in particular here it will be denoted as d _M (β, β _I ). Mahalanobis distance is defined as the square root of the vector difference value multiplied by the reciprocal of the covariance matrix. The distance used in the present invention is not limited to the Mahalanobis distance, and other known distances such as the Euclidean distance and the Manhattan distance can be used depending on circumstances.

In the next step 510, whether the distance between vectors is equal to or less than a predetermined value, that is,
Whether or not d _M (β, β _I ) <= δ _result is determined with a certain default value δ _result . If not, in step 512, the next coefficient of the coefficient vector α is selected, and the process returns to step 506. That is, in step 506, an interval is created based on the selected coefficient, and the differential equation is solved.

If it is determined in step 512 that d _M (β, β _I ) <= δ _result , the process proceeds to step 514, where the coefficient of interest α ₁ is set to 0 and the CAS 216 The process of solving the differential equation is performed again. _Assuming that the coefficient vector of the resulting solution is β ₀ , the value of d _M (β, β ₀ ) is calculated in step 516.

In step 518, it is determined whether d _M (β, β ₀ ) <= δ _result . Here, as the default value to be compared, a value different from that in step 510 may be used.

If it is determined in step 518 that d _M (β, β ₀ ) <= δ _result , it is determined in step 520 that the target coefficient is omitted. The decision information is stored in a predetermined location in main memory 106 and later used to provide a simplified differential equation 222.

On the other hand, if it is determined in step 518 that d _M (β, β ₀ ) <= δ _result is not satisfied, in step 522, the omission order of the target coefficient is lowered, that is, the coefficient is not actually omitted.

  After step 520 or step 522, the process goes to step 522 to determine whether all the coefficients that are components of the vector α are completed. If not, the process returns to step 506, and if so, the process proceeds to the process of the flowchart of FIG.

  In step 602 of FIG. 6, it is determined whether the system needs to consider stability. A system that does not require consideration of stability is a system in which a feedback loop does not exist, and it is known in advance that the output gradually decreases when there is no input.

  If the system doesn't need stability considerations. The process ends immediately.

  If it is determined in step 602 that the system needs to take stability into account, the process proceeds to step 604 where the stability of the system including the simplified formula is determined. Although any method known in the art can be used as the stability determination method here, the most typical is the Nyquist determination method. The Nyquist determination method is described in the literature of automatic control theory and is not the gist of the present invention.

  If the system is a discrete system, a determination method based on the eigenvalues of the state matrix can be used.

  Thus, if it is determined in step 606 that the system containing the simplified expression is stable, the process ends.

If it is determined in step 606 that the system containing the simplified equation is not stable, then in step 608 the coefficient vector distance between β _I and β calculated when a certain coefficient of α is returned. In descending order of the magnitude of d _M (β, β _I ), the coefficient which is the component of α is returned to the simplified formula, and the stability of the system is judged again at step 610. This stability determination method may be the same as the method in step 604.

  As a result, when it is determined in step 610 that the system is stable, the process ends. If it is determined in step 610 that the system is unstable, the next coefficient is selected in descending order of the distance between coefficient vectors in step 612, and the process returns to step 608.

  Although not explicitly shown in the flowchart of FIG. 6, if all the coefficients are returned and the system does not become stable, an error ends.

Eventually, as a result of the processing of FIG. 5 and FIG. 6, the following simplified mathematical expression 222 is obtained in which some of the Volterra series expansion terms of P (x), Q (x), and R (x) are omitted. .

  In the process of FIG. 5, it is likely that the solution of the differential equation based on the interval coefficient in step 506 is not obtained, and the solution is suddenly compared in step 514 with the target coefficient set to zero. However, without finding a solution of the differential equation based on the interval coefficient, if the solution is obtained with the target coefficient set to zero in step 514, there is a possibility of falling into an unstable local solution. Therefore, it is necessary to obtain a differential equation solution based on the interval coefficient.

  Thus, when the following simplified formula 222 is obtained, it is injected into the original block by the formula injection module 224, as shown in FIG. 3, or, as shown in FIG. It is converted into a block diagram by a conversion module 226 into a diagram.

  In the embodiment described above, the coefficient of the differential equation is expanded into a Volterra series at Step 502, the solution of the differential equation is expanded at Step 504, and the solution of the differential equation as a result of the interval analysis at Step 506 is solved. Volterra series expansion is performed, and the solution of the differential equation is also expanded by Volterra series in Step 514. However, the present invention is not limited to this, and it should be understood that the following modifications are also within the scope of the present invention. .

  First, it is possible to perform an interval analysis as it is without applying Volterra series expansion to the coefficients of the differential equation, and to apply Volterra series expansion to the solution of the differential equations. This is used when the dynamics of the system are known to some extent but the behavior of the differential equation solution is not well understood. In this case, the coefficient of the differential equation is not series-expanded in step 502, the solution of the differential equation is expanded in step 504, and the interval analysis in step 506 is applied to the coefficient that is not series-expanded. The solution of the differential equation is expanded by the Volterra series. In Step 514, the solution of the differential equation is expanded by the Volterra series.

  Next, interval analysis is performed as it is without applying Volterra series expansion to the coefficients of the differential equation, and processing without applying Volterra series expansion to the solution is also possible. This is used when the dynamics of the system is known to some extent and the behavior of the differential equation solution is quite predictable. In this case, the coefficient of the differential equation is not series-expanded in step 502, and the solution of the differential equation is not expanded in Volterra series in step 504. The interval analysis at step 506 is also applied to the coefficients that are not subjected to series expansion, and the solution of the resulting differential equation is not expanded to Volterra series. Even in step 514, the solution of the differential equation is not expanded to the Volterra series. In this case, the coefficient vector of the solution is created and compared in a form that is not expanded by the Volterra series.

  Furthermore, although the interval analysis is performed by applying Volterra series expansion to the coefficients of the differential equation, the solution of the differential equations can be processed without applying Volterra series expansion. This is not the case, but is adopted when the dynamics of the system is fairly unknown, while the behavior of the differential equation solution is quite predictable. In this case, the coefficient of the differential equation is expanded into a Volterra series at Step 502, but the solution of the differential equation is not expanded at Step 504. The interval analysis of the coefficients is applied to the coefficients subjected to the Volterra series expansion, and the solution of the differential equation as a result of the interval analysis in Step 506 is not expanded to the Volterra series. Even in step 514, the solution of the differential equation is not expanded to the Volterra series. In this case, the coefficient vector of the solution is created and compared in a form that is not expanded by the Volterra series.

  Next, the validity determination processing of the block diagram converted from the simplified mathematical expression 222 will be described with reference to the flowchart of FIG. This process is performed by the genus determination module 228.

  In step 702 of FIG. 7, the genus determination module 228 assigns a number to each block in the block diagram, and if the number of blocks is N, creates an N × N zero matrix.

  In step 704, if the genus determination module 228 is directed from the I-th block to the J-th block, the genus determination module 228 performs the process of setting the IJ element of the matrix to 1 for all inter-block connections.

  In step 706, the genus determination module 228 determines the genus of the graph using the matrix information corresponding to the graph representation generated from the block diagram. This algorithm is not particularly limited. For example, ML Furst, JL Gross, and LA McGeoch, “Finding a Maximum-Genus Graph Imbedding”, Journal of ACM, Vol. 35, No. 3, July 1988, pp. 523- The algorithm described in 534 is used.

  As a result, when it is determined in step 708 that the genus is smaller than 2, the process proceeds to step 710 and is determined to be valid in the block diagram. This may cause the system to display the resulting message on the display 114.

  If it is determined in step 712 that the genus is 2 or more and less than 7, a mathematical expression is recommended in step 714 because of the possibility of instability due to the loop. Again, the resulting message may be displayed on the display 114 by the system.

  If it is determined in step 712 that the genus is 7 or more, the vector operation is connected in step 716, but formula description or block division is recommended because of the possibility of too complicated connection. Again, the resulting message may be displayed on the display 114 by the system.

を最小化するH2最適コントローラを設計する問題である。 Next, an example of plant control will be described with reference to FIG. This example

It is a problem to design an H2 optimal controller that minimizes.

In this example, the problem is solved based on the following assumptions.
-Not all plant factors are required for the next controller design.
-If there is a situation where the state variables used in the controller can tolerate a few percent error, the controller structure can be simplified if there are elements in the matrix A and B that can be made zero.
-In fact, it is recommended from the present invention that the coefficients marked in Fig. 8 may be zero when Q and R are scalar matrices and a 5% deviation is allowed compared to the state variable when the coefficients are not omitted. Is displayed.
-Matrix C was not considered here because it does not affect state variables or controller design.
-The H2 controller was compared using a Kalman filter.
-In addition, design parameters included in the Q and R of the evaluation function can also find similar simplification possibilities, which may further simplify the controller.

In fact, if the transfer function matrix-related part of the plant is calculated by (zI-A) ^-1 B, each element of 4 rows and 2 columns of the given controlled object will be a (3rd / 4th) function, but simplified As a result, the element of 3 rows and 2 columns becomes a function of (second order / fourth order), and the efficiency at the time of mounting can be expected by reducing the order.

  That is, if the mathematical formula is simplified according to the present invention, the number of sensors and wirings can be reduced by reducing the order and coefficient by optimization, and the mounting cost can be reduced. As a result, it is possible to obtain an effect that a high-speed controller implementation is highly likely to be obtained by optimization.

  The present invention has been described based on the specific embodiments. However, the present invention is not limited to the specific embodiments, and can be applied to various configurations and techniques such as various modifications and substitutions obvious to those skilled in the art. I want you to understand. For example, the present invention is not limited to a specific processor architecture or operating system.

102 System path 104 CPU
110 Keyboard 112 Mouse 114 Display 106 Main Memory 108 Hard Disk Drive 202 Block 202 Modeling System 206 Source Model File 208 Source Code 210 Formula Extraction Module 212 Formula Conversion Module 214 Section Analysis Module 216 CAS
220 Stability determination module 224 Formula injection module 226 Conversion module 228 Genus determination module

Claims (30)

A modeling system control method for designing by computer processing,
Obtaining a mathematical formula from the model to be designed;
Obtaining a first solution from the equation;
Obtaining a second solution with one coefficient as an interval in the series;
The first solution coefficient is a first vector, the second solution coefficient is a second vector, and a first distance between the vectors is determined;
In response to the first distance being less than or equal to a predetermined value, obtaining a third solution with the one coefficient being zero; and
Determining a second distance between the first vector and the third vector, wherein the coefficient of the third solution is a third vector;
Determining that the term of the one coefficient in the equation is omissible in response to the second distance being equal to or less than a predetermined value;
Modeling system control method.   The method of claim 1, wherein coefficients of the mathematical formula are expanded by a Volterra series before obtaining a solution of the mathematical formula.   The method according to claim 1, wherein a solution of the mathematical expression is obtained as a Volterra series expansion solution.   The method of claim 1, wherein the distance is a Mahalanobis distance.   The method of claim 1, wherein the modeling system is a modeling system that generates a block of SysML.   6. The method of claim 5, further comprising: extracting a mathematical expression from the block; and injecting the mathematical expression of the mathematical expression with the term omitted.   The method of claim 1, wherein the modeling system is a modeling system that generates a block diagram.   8. The method of claim 7, further comprising: converting the block diagram into a mathematical formula; and transforming the mathematical formula of the mathematical formula with the term omitted.   9. The method of claim 8, further comprising determining a genus of the block diagram converted from the mathematical formula. A modeling program for designing by computer processing,
The computer,
Obtaining a mathematical formula from the model to be designed;
Obtaining a first solution from the equation;
Obtaining a second solution with one coefficient as an interval in the series;
The first solution coefficient is a first vector, the second solution coefficient is a second vector, and a first distance between the vectors is determined;
In response to the first distance being less than or equal to a predetermined value, obtaining a third solution with the one coefficient being zero; and
Determining a second distance between the first vector and the third vector, wherein the coefficient of the third solution is a third vector;
Determining that the term of the one coefficient in the equation is omissible in response to the second distance being equal to or less than a predetermined value;
Modeling program.   The program according to claim 10, wherein the coefficient of the mathematical formula is expanded in series before obtaining the solution of the mathematical formula.   The program according to claim 10, wherein the solution of the mathematical expression is obtained as a series-expanded solution.   The program according to claim 12 or 11, wherein the series expansion is a Volterra series expansion.   The program according to claim 10, wherein the distance is a Mahalanobis distance.   The program according to claim 10, wherein the modeling program includes generating a block of SysML.   The program according to claim 15, further comprising: extracting a mathematical expression from the block; and injecting into the book a mathematical expression in which the term is omitted.   The program according to claim 10, wherein the modeling program includes generating a block diagram.   The program according to claim 17, further comprising: converting the block diagram into a mathematical formula; and converting the mathematical formula of the mathematical formula from which a term is omitted into a block diagram.   The program according to claim 18, further comprising a step of obtaining a genus of the block diagram converted from the mathematical expression. A modeling system for designing by computer processing,
A means to create or edit a model to be designed;
Means for obtaining a mathematical formula from the model;
A calculation means having a function of obtaining a solution of the mathematical formula;
Means for causing the calculation means to calculate by applying the interval of the term of the formula;
Means for determining a distance between two different solutions by the calculating means;
A means for simplifying the mathematical expression by omitting the mathematical expression;
In response to the distance between the solutions being less than a predetermined distance, simplifying the formula by means of simplifying the formula;
Modeling system.   21. The system according to claim 20, wherein the calculation unit has a function of series expansion of the coefficient of the mathematical formula and the calculation result.   The system according to claim 21, wherein the calculating means uses a series expansion term when applying the term interval of the mathematical expression.   The system of claim 21, wherein the means for determining the distance between the two solutions determines the distance between the series expanded terms.   The system according to claim 23 or claim 22, wherein the series expansion is a Volterra series expansion.   21. The system of claim 20, wherein the distance is a Mahalanobis distance.   21. The system of claim 20, wherein the modeling system includes means for generating a SysML block.   27. The system of claim 26, further comprising: means for extracting a mathematical expression from the block; and means for injecting the mathematical expression of the mathematical expression with the term omitted.   21. The system of claim 20, wherein the modeling system includes means for generating a block diagram.   29. The system of claim 28, further comprising means for converting the block diagram into a mathematical expression and means for converting the mathematical expression of the mathematical expression with the term omitted.   30. The system of claim 29, further comprising means for determining a genus of the block diagram converted from the mathematical expression.

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